Simplify the following expression: $y = \dfrac{90a^3 - 20a^2}{20a^3}$ You can assume $a \neq 0$.
Solution: Find the greatest common factor of the numerator and denominator. The numerator can be factored: $90a^3 - 20a^2 = (2\cdot3\cdot3\cdot5 \cdot a \cdot a \cdot a) - (2\cdot2\cdot5 \cdot a \cdot a)$ The denominator can be factored: $20a^3 = (2\cdot2\cdot5 \cdot a \cdot a \cdot a)$ The greatest common factor of all the terms is $10a^2$ Factoring out $10a^2$ gives us: $y = \dfrac{(10a^2)(9a - 2)}{(10a^2)(2a)}$ Dividing both the numerator and denominator by $10a^2$ gives: $y = \dfrac{9a - 2}{2a}$